Genetic endowments
and wealth inequality

Barth, Papageorge, and Thom (2020) take aways

• Gene-wealth gradient exists: EA score predicts wealth at retirement
• Gene-wealth gradient⇐ education, income, bequests, parents’ education, but does not explain fully
• Gene-wealth gradient→0 when stock ownership is added
  • EA score \(\SIM\) risk torelance, longevity, stock ownership, precision in macroeconomic risk perception
• HHs without DB pension: gene-wealth gradient↑

SNP, polygenic score

.
└── Chromosome
    └── DNA
        └── Gene
            └── Genome

• Base pairs differ between people in less than 1% (15 million) locations
  
• Single-nucleotide polymorphism (SNP) = such location
  • 2 chromosomes per person: AT-AT, GC-GC, AT-GC or 0, 2, 1 (reference = GC)

Twin studies

• Estimate how much genetic factors collectively matter for explaining variations of a trait
  • Collectively: Unit = group level aggregation
  • Explaining variations: Variance decomposition
• Do not reveal which SNP is correlated

Polygenic score of \(i\) for the outcome \(Y\) = “Educational attainment (EA) score”

\[ PGS_{i}=\sum_{j=1}^{J}\tilde{\beta} SNP_{ij} \]

• Use Bayesian LDpred procedure to correct for correlations in \(\tilde{\beta}_{j}\)

• Use all SNPs: Better out-of-sample results than using only SNPs with genome-wide significance \(p\) value \(< 5*10^{-8} =\) .0000005%

• PGS is considered to be a predictor of individual fixed effects

  • HRS sample: covariance with EA score / total schooling years variance = 10.6%
  • Edu attainment SNPs \(\SIM\) biological process of brain development, cognition (Okbay et al. 2016; Lee et al. 2018)
  • Edu attainment SNPs \(\SIM\) cognition SNPs (Okbay et al. 2016)

Gene-wealth gradient \(\gamma\) with education control

\[ \begin{aligned} W_{i} &= \bftheta'\bfx_{i}+\gamma PGS_{i}+\eta Y_{i}+e_{i},\\ &= \bftheta'\bfx_{i}+\gamma PGS_{i}+\frac{\eta}{J}\left\{PGS_{i}+\sum_{j=1}^{J}\left(\bfmu'_{j}\bfx_{i}+\tilde{\epsilon}_{ij}\right)\right\}+e_{i},\\ &= \bftheta'\bfx_{i}+\left(\gamma+\frac{\eta}{J}\right)PGS_{i}+\frac{\eta}{J}\sum_{j=1}^{J}\left(\bfmu'_{j}\bfx_{i}+\tilde{\epsilon}_{ij}\right)+e_{i},\\ &\simeq \left(\bftheta'+\eta\bar{\bfmu}'\right)\bfx_{i}+\gamma PGS_{i}+\eta\bar{\tilde{\epsilon}}_{i}+e_{i}. \end{aligned} \] where \[ JY_{i} = PGS_{i}+\sum_{j=1}^{J}\left(\bfmu'_{j}\bfx_{i}+\tilde{\epsilon}_{ij}\right). \]

Because \(\cov[SNP_{ij}, \epsilon_{ij}]> 0\), in general, we have \(\cov[PGS_{i}, \bar{\tilde{\epsilon}}_{i}]> 0\).

Interpretation

• Correlation, not causality: Outcomes ⇐ gene + environment (endogenous)
• Attenuation due to measurement errors in \(\hat{\beta}_{j}\)
• Linearity assumption → likely underestimation of gene contributions (relative to twin studies)
• Population stratification: Ethnic-group fixed effects ⇐ gene, environment
  • Including first (10) principal components of SNP data as covariates is shown to control geographic variations
• External validity is up to HRS ancestral composition

Data

1. Health and retirement survey: Age > 50 + partners, genetic samples 2006, 2008
   • All households with at least one individual with genetic European
   • “Retired households” in 1996, 1998, 2002, 2004, 2006, 2008, 2010
   • Households with 1-2 members, drop same sex HHs
   • Household-year observations of both members 65-75 years old
   • Self-reported earnings
     
2. Social security administration data
   • Income data, top coded

our sample comprises households for whom wealth data are most likely to be both accurate and comprehensive.

• All pension, annuity, social security income, defined-contribution retirement plans
• Net value of housing, private businesses, vehicles, financial assets (cash, checking account, saving account, CD, stocks, mutual funds, trusts, other)
• Winsorize at 1st and 99th percentiles of log real total wealth

Standard controls

age, sex of FR, calendar time, family member age-sex dummies and interactions

Full education controls

education-age-sex dummies and interactions

Selection biases

1. Into genotyping: Older, more educated, more females, wealthier (Table S1)
   • Education \(\SIM\) genotyping ⇒ individuals with low EA scores have higher than average education ⇒ attenuates EA score \(\SIM\) education gradient

Selection biases

2. Of using retired households: More precise wealth but smaller sample size/more selection (Table 3)
   • Selection results in more males, older in high EA scores ⇐ (Male) higher EA scorers live longer, but modest in size (Panel A)
   • Age band of retired HHs ↑ than main sample ⇒ q4-q1 differences (more selection) ↑ ⇒ EA score \(\SIM\) education gradient ↑ (Panel A vs. B)
   • \(+\)non-retired HHs ⇒ q4-q1 differences ↓ (less selection) ⇒ EA score \(\SIM\) education gradient ↓ (Panel A vs. C)
   • Smaller degree of selection leads to smaller q4-q1 differences
   • But larger measurement errors in wealth (\(\because\) pensions, etc. are not measured)

However, the magnitudes of these differences are similar and relatively modest across alternate samples. Restricting our sample to retired households balances concerns about sample selection and measurement error. (p.19)

Results

Robust to:

• Changes in sample and definitions: HRS sampling weights, only 1 HH-year per sample, only coupled HHs, different age, complicated function of incomes, excluding retirement and housing wealth, different version of EA score
• Adding: cognitive ability, number of children, death of HH member, years since retirement

Gene-environment correlations

Additional mechanisms

EA score↑

EA score↑

Conclusions

• Previous studies: \(\corr\)[EA scores, education]\(>0\)
• This study: \(\corr\)[EA scores, wealth|education, parents]\(>0\)
• EA scores \(\SIM\) probabilistic thinking ⇒ human capital accumulation heterogeneity
  • Teaching probability may make human capital more homogenous?
  • Not necessarily, gene-wealth gradient is a biased estimate ← environment
  • But it hints something can be done there

Conclusions

• “Ignoring heterogeneity in EA scores may place too much weight on education and inheritance”
  • Using HH (parent-multiple children) fixed effect estimator should prevent this?
• Intervention changes the nature contribution (gradient size): DB pensions

感想

• 「貧しさは遺伝する」?…PGSを使って資産との相関を計測した研究
• 強い根拠はないにせよ、介入ポイントを議論したのは素晴らしい
• Gene-wealth gradient = \(\corr\)[PGS, wealth|(endogenous) variables]
  
• 偏相関が小さくなるポイント: 株式所有 ⇐ longer time horizon, optimism
• 偏相関が大きくなるポイント: 確定給付年金
  • 株式所有と確定給付年金を加えたら偏相関は?
• 金融教育?
• 確定給付年金をもっと広く手厚く(できるのか?)
• 計量: 個人固定効果の中身をPGSとそれ以外に分解